I think think the program is in error. If there was ever a trail that was accessible to vehicles, it was way back in the days when the trail was used by miners. Perhaps it's a leftover from some old USGS maps. I found a link about the Tanner trail
here . It doesn't mention anything about a 4WD trail crossing the hiking trail. From my experience with the Grand Canyon NP, they really don't allow anything except people and mules/horses below the rim(except the occasional helicopter that goes the Phantom Ranch). Your best bet to get a final answer would be to call the Park itself. I would highly recommend taking at least a day hike, if not an overnight hike into the Canyon. It's been one of the best experiences I've had. There are more incredible views from below the rim than you will ever see from the rim. I'm not talking about just taking an hour walk down Bright Angel trail, but a good half to full day hike. Be prepared in August for hot weather below the rim and also whereever you are at in AZ and UT, be prepared for monsoon rains. I'm not sure what you experience with deserts are, but they can really sap your water quickly. Add that to the elevation and you can run into dehydration quickly if you not carefull.
Keep me posted on your progress and plans, I'd love to see what finally decide to do. Perhaps if the timeframe works out, we can meet up.
If you are planning on coming out in mid-August, have you considered bumping your trip to corespond with GOX 3 in Ouray, CO? There is some great 4 wheeling around Ouray.
Andy